It is normal, but it is not acceptable. Two things: Quick jerky movements from your part trigger her prey drive and get her to want to lunge, jump snap at the toy that you are trying to snatch up from the ground before she nails your hand, and the same thing when you have the toy in your hand and you keep snatching it away because she is catching/biting you in her effort to get the toy. The growly behaviour is resource guarding, and also not acceptable. So to stop this, you have to be aware of how your energy and jerky, snatchy, quick movements triggers a reaction from her, and let her know that all resources are yours, and you allow her to play with YOUR toys.
So rehabilitation time for Roger and puppy! Teach her to sit and wait for the toy. At first, a mili-second of a sit and an instant of focus on you (not the toy) and you reward her by giving her the toy. Then gradually a bit more. It may take a while for her to get it, but keep at it. Teach the basics with food if she gets to amped up for a toy and can't concentrate. When she knows the routine well, then you can introduce the same exercise with a toy.
Now watch how YOU move and what energy you give out that triggers her prey drive and brings out that jumpy/bitey behaviour. If you are going to pick up a toy, don't snatch it up like you are trying to compete against her like it's a race as to who gets it first. Walk up like you own the world, own the house, own the toy (and except for the world, you do own everything in your house), and smoothly with confidence and no hesitation (and NO jerky movement), just bend down without even looking at her, pick it up and walk away.
She won't really change instantly when you start this. She will need to know a sit-stay command, and a leave it command. If she jumps and snatches or bites your hand, everything stops. Give a NO, turn your back walk away, put the toy away, fun is over.
For example, my dog brings me toys and pushes them into my hand to play with him. He will follow me around nosing the toy and looking at me hoping that I will play fetch or tug with him. After we are done, I take the toy, say "My ball" (or tug or whatever), and hold it up close to my body, or put it in my pocket, and he knows I've now taken possession of MY ball, and he'll saunter off to annoy my older dog or find a stick to chew on.
So in short -
- growling can be a play growl, or it can be resource guarding. If play growl, you can ignore it, but considering the context, I think it is more resource guarding. Introduce more obedience commands (at her age, a sit and a some focus is fine), before she gets ANYTHING! Food, toys, attention, petting, a walk. This sets her up to defer to you, and understand that you expect certain behaviours from her before she gets attention and fun. If you are not familiar with NILIF (Nothing in Life is Free), google it and implement the system into your daily routine.
- Watch YOUR energy, do not trigger her prey drive with jerky, quick movements when going for her toy. If she is jumping at your hand to get the toy. Keep your energy neutral, keep your hands quiet, get her to sit and focus, then throw the toy. Eventually she should be offering you a sit and the focus to get you to throw the toy for her without you even asking.
Also agree with Jenna - 35 minutes a day is not enough, no wonder she is all riled up and snapping. At that age you can walk her for miles!! Hiking, swimming, climbing! Classes to exercise her mind and teach her to behave. Great for bonding and teaching her to mind.